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Practice

7.15.5 Practice

7.15.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Select three quadratic expressions written in vertex form.
  1. y = ( x − 2 ) 2 + 1
  2. y = x 2 − 4
  3. y = x ( x + 1 )
  4. y = ( x + 3 ) ( x + 3 )
  5. y = ( x − 4 ) 2 + 6

Examine the following two equations and use them to answer questions 2 – 5. One defines function m and the other defines function p .

  • m ( x ) = x ( x + 6 )
  • p ( x ) = ( x + 3 ) 2 − 9
  1. How do you know that the expressions defining m and p are equivalent?
  1. Both expressions are equal to x 2 − 3 .
  2. Both expressions are equal to 2 x + 6 .
  3. Both expressions are equal to x 2 − 6 x .
  4. Both expressions are equal to x 2 + 6 x .
  1. Recall m ( x ) = x ( x + 6 ) and p ( x ) = ( x + 3 ) 2 − 9 . What is the x -coordinate of the vertex of the graph of m ? 
  1. Recall m ( x ) = x ( x + 6 ) and p ( x ) = ( x + 3 ) 2 − 9 . What is the y -coordinate of the vertex of the graph of m ? 
  1. Recall m ( x ) = x ( x + 6 ) and p ( x ) = ( x + 3 ) 2 − 9 . What are the x -intercepts of the graph of p ? 
  1. ( 0 , 0 ) and ( 0 , 6 )
  2. ( 0 , 0 ) and ( 0 , − 6 )
  3. ( 0 , 0 ) and ( 6 , 0 )
  4. ( 0 , 0 ) and ( − 6 , 0 )

For questions 6 – 11, enter the coordinates of the vertex of the graph that represents the equation.

  1. Find the coordinates of the vertex for the equation y = ( x − 3 ) 2 + 5 .
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Find the coordinates of the vertex for the equation y = ( x + 7 ) 2 + 3 .
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Find the coordinates of the vertex for the equation y = ( x − 4 ) 2 .
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Find the coordinates of the vertex for the equation y = x 2 − 1 .
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Find the coordinates of the vertex for the equation y = 2 ( x + 1 ) 2 − 5 .
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Find the coordinates of the vertex for the equation y = − 2 ( x + 1 ) 2 − 5 .
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?

For questions 12 – 14, answer the questions about the x - and y -coordinates of the vertex, and whether the function opens up or down.

  1. For function f ( x ) = ( x − 4 ) 2 − 5 :
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. For the function f ( x ) = ( x − 4 ) 2 − 5 , does the graph open up or down?
  1. Up
  2. Down
  1. For function g ( x ) = − x 2 + 5 :
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. For the function g ( x ) = − x 2 + 5 , does the graph open up or down?
  1. Up
  2. Down
  1. For function h ( x ) = 2 ( x + 1 ) 2 − 4 :
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. For the function h ( x ) = 2 ( x + 1 ) 2 − 4 , does the graph open up or down?
  1. Up
  2. Down